Conveners
Workshop on NCG: Session 1
- Anna Pachol (Queen Mary University of London)
Workshop on NCG: Session 2
- Anna Pachol (Queen Mary University of London)
Workshop on NCG: Session 3
- Latham Boyle (Perimeter Institute)
Workshop on NCG: Session 4
- Koen van den Dungen (SISSA)
The standard model contains a rather strong hint that -- instead of being simply an ordinary continuous 4D manifold -- spacetime is actually the product of a 4D manifold and a certain discrete/finite space (i.e. there are discrete/finite "extra dimensions"). I will introduce this idea and the evidence for it in a simple way. I will describe recent progress in this direction, as well as some...
We present a Spin group GUT inspired from Noncommutative Geometry that breaks down to the Standard model and reproduces the results of the Spectral Model. We believe this model explains some of the less intuitive axioms of spectral triples.
I will introduce the framework of non-associative geometry as a natural extension of Connes' non-commutative geometry. I will then give worked examples and describe applications in particle physics.
We study a noncommutative analogue of a spacetime foliated by spacelike hypersurfaces. First, we consider a spacetime given by a family of spacelike hypersurfaces (M,g_t) parametrised by the real line. We then construct a 'product spectral triple' from the corresponding family of canonical spectral triples over M and the lapse function. This product spectral triple reproduces the canonical...
TBA
We introduced few years ago a new notion of causality for noncommutative spacetimes directly related to the Dirac operator and the concept of Lorentzian spectral triple. This notion of causality corresponds to the usual one for commutative spectral triples and could be extended in order to get a full Lorentzian metric. We explored the noncommutative causal structure of several toy models as...
Noncommutative geometry, as the generalised notion of geometry, allows us to model the quantum gravity effects in an effective description without full knowledge of quantum gravity itself. On a curved space one must use the methods of Riemannian geometry – but in their quantum version, including quantum differentials, quantum metrics and quantum connections – constituting quantum geometry. The...
The recent formalism of Poisson-Riemannian geometry provides a useful approach to studying noncommutative differential geometry. Utilizing functional methods, it allows for the construction of a quantum metric and quantum Levi-Civita connection up to first order in deformation based on a classical metric, Poisson tensor and compatible connection. I will give a brief overview of the formalism...
